A complex representation \((\pi ,V)\)  of a finite group \(G\)  is called orthogonal if it preserves a non-degenerate symmetric bilinear form. An orthogonal representation \(\pi \)  is called spinorial if it can be lifted to \(\mathrm {Pin}(V)\) , the topological double cover of \(\mathrm {O}(V)\) .
See [1]} for reference.
